The conformal Carrollian field theories that we are discussing in this work are also BMS-invariant field theories. This stems from the isomorphism between these groups [1]}, [2]}, [3]}. This isomorphism was discovered following an even more startling observation of the isomorphism between Galilean conformal algebras and the BMS algebra [4]}. Field theories defined on these Carrollian backgrounds suffer from the absence of a non-degenerate metric; the theories are defined on a fibre-bundle structure rather than a (pseudo-) Riemmannian one. Our task of investigating Weyl symmetry would thus be complicated by this feature. In what follows, we shall be exclusively focussing on conformal Carrollian or BMS invariant theories in 2 spacetime dimension.
